On the shellability of the order complex of the subgroup lattice of a finite group
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- by John Shareshian PDF
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Abstract:
We show that the order complex of the subgroup lattice of a finite group $G$ is nonpure shellable if and only if $G$ is solvable. A by-product of the proof that nonsolvable groups do not have shellable subgroup lattices is the determination of the homotopy types of the order complexes of the subgroup lattices of many minimal simple groups.References
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Additional Information
- John Shareshian
- Affiliation: California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
- MR Author ID: 618746
- Email: shareshi@math.miami.edu
- Received by editor(s): February 18, 1999
- Received by editor(s) in revised form: May 1, 1999
- Published electronically: March 12, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2689-2703
- MSC (1991): Primary 06A11; Secondary 20E15
- DOI: https://doi.org/10.1090/S0002-9947-01-02730-1
- MathSciNet review: 1828468